Abstract
A creep model based on the damage mechanics is proposed in this study to describe the three-stage creep deformation of rocks under conventional triaxial loading conditions. The proposed model has a simple form as it is based on the mechanism which assumes that the time-dependent creep behavior of rocks is solely described by the damage evolution. Verification of the proposed model against the creep tests shows that the model can reflect the three-stage creep behavior under higher stress levels as well as the elastic behavior under lower stress levels using the same model equations. The features of the proposed model include: (1) Simple mathematical form as it contains only one strain component without strain partitioning, and one set of equations to predict the creep deformation for all stress levels; and (2) The model requires only four parameters. All these features make the proposed model simple to use and easy to implement.
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References
Amitrano D, Helmstetter A (2006) Brittle creep, damage, and time to failure in rocks. J Geophys Res: Solid Earth. https://doi.org/10.1029/2005jb004252
Baud P, Meredith P (1997) Damage accumulation during triaxial creep of Darley Dale sandstone from pore volumetry and acoustic emission. Int J Rock Mech Min Sci Geomech Abstr 34:1–8
Boukharov GN, Chanda MW, Boukharov NG (1995) The three processes of brittle crystalline rock creep. Int J Rock Mech Mining Sci Geomech Abstr 32:325–335. https://doi.org/10.1016/0148-9062(94)00048-8
Chen L, Wang CP, Liu JF, Liu YM, Liu J, Su R, Wang J (2014) A damage-mechanism-based creep model considering temperature effect in granite. Mech Res Commun 56:76–82. https://doi.org/10.1016/j.mechrescom.2013.11.009
Davy P, Hansen A, Bonnet E, Zhang S-Z (1995) Localization and fault growth in layered brittle-ductile systems: implications for deformations of the continental lithosphere. J Geophys Res: Solid Earth 100:6281–6294. https://doi.org/10.1029/94jb02983
Heap MJ, Baud P, Meredith PG, Bell AF, Main IG (2009) Time-dependent brittle creep in Darley Dale sandstone. J Geophys Res: Solid Earth. https://doi.org/10.1029/2008jb006212
Jiang Q, Qi Y, Wang Z, Zhou C (2013) An extended Nishihara model for the description of three stages of sandstone creep. Geophys J Int 193:841–854. https://doi.org/10.1093/gji/ggt028
Katsuki D, Gutierrez M (2011) Viscoelastic damage model for asphalt concrete. Acta Geotechnica 6(4):231–241
Kranz RL (1980) The effects of confining pressure and stress difference on static fatigue of granite. J Geophys Res: Solid Earth 85:1854–1866. https://doi.org/10.1029/JB085iB04p01854
Lockner D (1993) Room temperature creep in saturated granite. J Geophys Res: Solid Earth 98:475–487. https://doi.org/10.1029/92jb01828
Main IG (2000) A damage mechanics model for power-law creep and earthquake aftershock and foreshock sequences. Geophys J Int 142:151–161. https://doi.org/10.1046/j.1365-246x.2000.00136.x
Masuda K (2001) Effects of water on rock strength in a brittle regime. J Struct Geol 23:1653–1657. https://doi.org/10.1016/S0191-8141(01)00022-0
Mijovic I (1994) An introduction to the mechanical properties of solid polymers, I. M. Ward and D. W. Hadley, John Wiley & Sons, Chichester, UK, soft cover £19.95. Polym Advan Technol 5:619–619. https://doi.org/10.1002/pat.1994.220050929
Nishihara M (1952) Creep of shale and sandy-shale. J Geol Soc Jpn 58:373–377
Pan YW, Dong JJ (1991) Time-dependent tunnel convergence—I. Formulation of the model. Int J Rock Mech Mining Sci Geomech Abstr 28:469–475. https://doi.org/10.1016/0148-9062(91)91122-8
Ranalli G (1995) Rheology of the Earth. 2nd edn. Chapman & Hall, London
Scholz CH (1972) Static fatigue of quartz. J Geophys Res 1896–1977(77):2104–2114. https://doi.org/10.1029/JB077i011p02104
Wang G (2004) A new constitutive creep-damage model for salt rock and its characteristics. Int J Rock Mech Min 41:61–67. https://doi.org/10.1016/j.ijrmms.2004.03.020
Wang X (2016) Experimental study and constitutive model of creep for rock materials. Master’s Degree of Engineering, Chongqing University
Yang W, Zhang Q, Li S, Wang S (2014) Time-dependent behavior of diabase and a nonlinear creep model. Rock Mech Rock Eng 47:1211–1224
Zhang XZ, Wang L, Zhang DJ (1999) An experimental study on rheological characteristics of Gabbro in EastMountain slope of Zhujiabaobao mine. J Chong Qing Univ (Nat Sci Edition) 22:99–103 (In Chinese)
Zhang XD, Li YJ, Zhang SG (2004) Creep study of soft rock and its engineering application. Chin J Rock Mech Engg 23:1635–1639 (In Chinese)
Zhou HW, Wang CP, Han BB, Duan ZQ (2011) A creep constitutive model for salt rock based on fractional derivatives. Int J Rock Mech Min 48:116–121. https://doi.org/10.1016/j.ijrmms.2010.11.004
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Ma, S., Gutierrez, M. A time-dependent creep model for rock based on damage mechanics. Environ Earth Sci 79, 466 (2020). https://doi.org/10.1007/s12665-020-09198-7
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DOI: https://doi.org/10.1007/s12665-020-09198-7